Sweeney D W, Vest C M
Appl Opt. 1973 Nov 1;12(11):2649-64. doi: 10.1364/AO.12.002649.
Numerical and analytical techniques are presented that allow three-dimensional, asymmetric, refractive index fields to be reconstructed from optical pathlength measurements, which can be obtained using multidirectional holographic interferometry. Analytical reconstruction techniques that have been used in radioaptronomy and electron microscopy for a number of years, and recently in interferometry, are presented in the context of interferometric applications in the refractionless limit. These techniques require that optical pathlength data be collected over a 180 degrees angle of view. The required pathlength sampling rate is discussed. An efficient numerical procedure is developed for direct inversion of the data. Several numerical techniques are developed that do not require that data be collected over a full 180 degrees angle of view. All such techniques require redundant data to achieve accurate reconstructions. The required degree of redundancy increases as the angle of view decreases. Numerical simulations using six different reconstruction techniques indicate that with a 180 degrees angle of view, all are capable of providing accurate reconstructions. Four of the techniques were used to analyze simulated interferometric data recorded over an angle of view of less than 180 degrees . Examples of reasonably accurate reconstructions using data with angles of view as low as 45 degrees are presented.
本文介绍了数值和分析技术，这些技术可根据光程测量结果重建三维非对称折射率场，而光程测量可通过多方向全息干涉测量法获得。文中介绍了多年来在射电天文学和电子显微镜中使用、最近在干涉测量中也开始使用的分析重建技术，这些技术是在无折射极限的干涉测量应用背景下提出的。这些技术要求在 180 度视角范围内收集光程数据。文中讨论了所需的光程采样率。开发了一种用于数据直接反演的高效数值程序。还开发了几种不需要在完整的 180 度视角范围内收集数据的数值技术。所有这些技术都需要冗余数据才能实现精确重建。所需的冗余度随着视角的减小而增加。使用六种不同重建技术进行的数值模拟表明，在 180 度视角下，所有技术都能够提供精确的重建结果。其中四种技术用于分析在小于 180 度视角范围内记录的模拟干涉测量数据。文中给出了使用视角低至 45 度的数据进行合理精确重建的示例。
